In an examination, 5%

Question

In an examination, 5% of the applicants were found ineligible and 85% of the eligible candidates belonged to the general category. If 4275 eligible candidates belonged to other categories, then how many candidates applied for the examination?

Options:

A . 28000

B . 30000

C . 32000

D . 33000

Answer: Option B

Answer : Option B

Explanation :

Let the number of candidates applied for the examination = x
Given that 5% of the applicants were found ineligible.
It means that 95% of the applicants were eligible (âˆ´ 100% - 5% = 95%)

$MF#%\text{Hence total eligible candidates = }\dfrac{95x}{100}$MF#%

Given that 85% of the eligible candidates belonged to the general category
It means 15% of the eligible candidates belonged to other categories(âˆ´ 100% - 85% = 15%)

$MF#%\begin{align}
&\text{Hence Total eligible candidates belonged to other categories} \\
&= \text{total eligible candidates}\times \dfrac{15}{100} = \dfrac{95x}{100} \times \dfrac{15}{100}\\
&= \dfrac{95x \times 15}{100 \times 100}
\end{align} $MF#%

Given that Total eligible candidates belonged to other categories = 4275

$MF#%\begin{align}
&\Rightarrow \dfrac{95x \times 15}{100 \times 100} = 4275\\\\
&\Rightarrow \dfrac{19x \times 15}{100 \times 100} = 855\\\\
&\Rightarrow \dfrac{19x \times 3}{100 \times 100} = 171\\\\
&\Rightarrow \dfrac{x \times 3}{100 \times 100} = 9\\\\
&\Rightarrow \dfrac{x}{100 \times 100} = 3\\\\
&\Rightarrow x = 3 \times 100 \times 100 = 30000\\
\end{align} $MF#%

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